KEY STEPS

Compendium on methods and tools to evaluate impacts of, and vulnerability and adaptation to, climate
change

Bruun Rule Description

Description

The first and best known model relating shoreline retreat to an increase in local sea level is that
proposed by Per Bruun (1962). The IPCC reports that 1 cm rise in sea level erodes beaches about 1 m
horizontally. This becomes a large issue for developed beaches that are less than 5 m from the ocean
(IPCC, 1998).

The Bruun rule states that a typical concave-upward beach profile erodes sand from the beach face and
deposits it offshore to maintain constant water depth. The Bruun rule can be applied to correlate
sea-level rise with eroding beaches. The Bruun rule estimates the response of the shoreline profile
to sea-level rise. This simple model states that the beach profile is a parabolic function whose
parameters are entirely determined by the mean water level and the sand grain size. The analysis by
Bruun assumes that with a rise in sea level, the equilibrium profile of the beach and shallow
offshore moves upward and landward.

The analysis is two-dimensional and assumes that,

The upper beach is eroded due to the landward translation of the profile;

The material eroded from the upper beach is transported immediately into the offshore and
deposited, such that the volume eroded is equal to the volume deposited;

The rise in the nearshore bottom as a result of deposition is equal to the rise in sea level,
thus maintaining a constant water depth in the offshore (SCOR, 1991).

Appropriate Use

The Bruun rule is only applicable for small scale local sites.

Scope

Over long stretches of coast, the Bruun rule and associated cross-shore transport models become
complex. There has been a number of critiques e.g. Cooper and Pilkey (2004).

Key Output

Shoreline recession (in metres relative to sea-level rise).

Key Input

An increase in sea level, (S), cross shore distance (L) to the water depth (h) taken by Bruun as the
depth to which nearshore sediments exist (depth of closure), and B is the height of the dune.

Ease of Use

Easy to use with numerous assumptions.

Training Required

Familiarity with the coastal zone being investigated.

Training Available

None

Computer Requirements

None, unless it is incorporated into a model.

Documentation

Originally proposed by Per Bruun in 1962.

International Studies

Bruun (1962, 1988)

Contacts for Framework, Documentation, Technical Assistance

See applications

Cost

No cost to use the Bruun rule.

Validity

Bruun rule has been applied but caution needs to be exercised where other factors influence sediment
budget or control profile.